LA 4.3 Least Squares

Main points:
• Multiple m2 x of x that reaches closest to y
○ Multiple is called the projection of y on the line spanned by x
○ Step from the tip of the projection m2 x to y is the residual vector r
○ m can only be estimated, the quality of estimation is indicated by the length of the residual vector r
• The fundamental problem of Linear Modeling
○ Least-squares curve-fitting with J parameters leads to projection onto subspaces spanned by J vectors.
§ The line y = m2 x is called the least squares fit to the data
○ The optimal linear combination is called the projection of the vector b on the subspace spanned by the vectors u1, . . ., uJ

Challenges:
I understood what the topic discussed in terms what is being solved but I didn’t understand the methods applied in the solving. I also had problems understanding the examples. In the first example I didn't understand how the m2 value (170/89) was obtained.

Reflection:
This topic area seems highly relevant because many social sciences have optimization problems. In my area of interest, economics, this section had even an example of the effect of advertising dollars on sales. This made the whole topic a lot more interesting to study, even I didn’t completely understand the examples.